Help me and plot the graph

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Answer

To plot the graph of y=f(x)=3x−x2y = f(x) = 3x - x^2, you will use the table of values calculated previously and the specified scale.

Graph of f(x) = 3x − x²

Use the left and right arrow keys to trace the curve, up and down to jump between key points, and plus and minus to zoom.

Key points of f(x) = 3x − x²
Pointxy
x-intercept00
Maximum1.52.25
x-intercept30
  • Points to plot: From the table in part a) of the previous question, you have the following points:

    xy−1−4001222304−4\begin{array}{|c|c|} \hline x & y \\ \hline -1 & -4 \\ 0 & 0 \\ 1 & 2 \\ 2 & 2 \\ 3 & 0 \\ 4 & -4 \\ \hline \end{array}
  • Scale: Use a scale of 2cm to represent 1 unit on both the x-axis and the y-axis. This means:

    • For the x-axis: Mark x=0x=0, then x=1x=1 will be 2cm to the right, x=2x=2 will be 4cm to the right, x=−1x=-1 will be 2cm to the left, and so on.
    • For the y-axis: Mark y=0y=0, then y=1y=1 will be 2cm upwards, y=2y=2 will be 4cm upwards, y=−1y=-1 will be 2cm downwards, and so on.
  • Plotting the points:

    1. Draw your x and y axes.
    2. Mark the scale on both axes according to the 2cm = 1 unit instruction.
    3. Plot each point from the table:
      • (−1,−4)(-1, -4)
      • (0,0)(0, 0) (the origin)
      • (1,2)(1, 2)
      • (2,2)(2, 2)
      • (3,0)(3, 0)
      • (4,−4)(4, -4)
  • Drawing the curve: Since f(x)=3x−x2f(x) = 3x - x^2 is a quadratic function with a negative coefficient for x2x^2 (i.e., a=−1a = -1), its graph is a parabola that opens downwards. Connect the plotted points with a smooth, continuous curve. The curve should be symmetrical. Remember that the maximum point (vertex) is at (1.5,2.25)(1.5, 2.25), as calculated in part d). This point should be the highest point on your curve.

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